A person may try to sound like they care or are interested in something you have confided but it is fake sincerity.
Me "I have been sick for days."
Them "Oh my, that sucks!" they say with fauxerity and they continue on by talking about themselves " OMG, I had to wear dirty socks today! I had to stay late at work. I...I...Me...Me...Me..."
That person has a bad case of fauxerity!